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An ordinary unambiguous integral representation for the finite propagator of a quantum system is found by starting of a privileged skeletonization of the functional action in phase space, provided by the complete solution of the…
This study introduces a mathematical framework to investigate the viability and reachability of production systems under constraints. We develop a model that incorporates key decision variables, such as pricing policy, quality investment,…
We study self-replicating molecules under externally varying conditions. Changing conditions such as temperature variations and/or alterations in the environment's resource composition lead to both non-constant replication and decay rates…
An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the finite-scale Hamiltonian dynamics is governed by…
We develop a computational method to learn a molecular Hamiltonian matrix from matrix-valued time series of the electron density. As we demonstrate for three small molecules, the resulting Hamiltonians can be used for electron density…
The dynamics generated by non-Hermitian Hamiltonians are often less intuitive than those of conventional Hermitian systems. Even for models as simple as a complexified harmonic oscillator, the dynamics for generic initial states shows…
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor fields that are invariant under the given…
Hamilton-Jacobi (HJ) reachability is a method that provides rigorous analyses of the safety properties of dynamical systems. This method has been successfully applied to many low-dimensional dynamical system models such as coarse models of…
We extend the work on optimal investment and consumption of a population considered in [2] to a general stochastic setting over a finite time horizon. We incorporate the Cobb-Douglas production function in the capital dynamics while the…
We consider one-dimensional classical time-dependent Hamiltonian systems with quasi-periodic orbits. It is well-known that such systems possess an adiabatic invariant which coincides with the action variable of the Hamiltonian formalism. We…
In this paper, we construct Hamilton-Jacobi equations for a great variety of mechanical systems (nonholonomic systems subjected to linear or affine constraints, dissipative systems subjected to external forces, time-dependent mechanical…
A tensor decomposition approach for the solution of high-dimensional, fully nonlinear Hamilton-Jacobi-Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The method combines a tensor train approximation…
This paper characterizes differentiable subgame perfect equilibria in a continuous time intertemporal decision optimization problem with non-constant discounting. The equilibrium equation takes two different forms, one of which is…
We connect Quantum Hamilton-Jacobi Theory with supersymmetric quantum mechanics (SUSYQM). We show that the shape invariance, which is an integrability condition of SUSYQM, translates into fractional linear relations among the quantum…
We study a stochastic branching model for a population structured by a quantitative phenotypic trait and subject to births, deaths, and mutations. In a regime of large population and small mutations, and in logarithmic scales of size and…
We study existence of solutions in the variational sense for a class of stochastic phase-field models describing moving boundary problems. The models consist of stochastic reaction-diffusion equations with singular diffusion forced by a…
We study continuous dependence estimates for viscous Hamilton- Jacobi equations defined on a network Gamma. Given two Hamilton-Jacobi equations, we prove an estimate of the C2-norm of the difference between the corresponding solutions in…
The constrained filed system, the scalar field coupled to two flavours of fermions through Yukawa couplings, is treated by using the Hamilton-Jacobi approach. The equations of motion are obtained as total differential equations in many…
Chemical relaxation phenomena, including photochemistry and electron transfer processes, form a vigorous area of research in which nonadiabatic dynamics plays a fundamental role. Here, we show that for nonadiabatic dynamics with two…
We generalize the Hamilton-Jacobi formulation for higher order singular systems and obtain the equations of motion as total differential equations. To do this we first study the constraint structure present in such systems.